(a) In a certain state, license plates have two letters followed by four digits. How many such license plates are possible?(b) If the state department of transportation decides to change the plates to have four letters followed by two digits, how many plates will now be possible?a) There aredifferent possible license plates with 2 letters followed by 4 digits.(Type a whole number.)

Answered: Image /qna-images/answer/94ad3aa2-8dbf-4ed7-b6c2-cffc3f08c203.jpg

Answered: (a) In a certain state, license plates…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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At a music festival, there are seven bands scheduled to play, numbered 1 through 7. a. How many different ways can these bands be arranged to perform? b. If band 3 is performing first and band 1 last, then how many ways can their appearances be scheduled? a. There are different ways to arrange the bands. (Simplify your answer.) b. If band 3 is performing first and band 1 last, there are different ways to arrange the bands. (Simplify your answer.) Enter your answer in each of the answer boxes.
1. A license plate begins with three letters and three numbers. If the possible letters are all vowels only, and the number choices for each digit will only be odd numbers, how many different license plates can be made if no letter and number is used more than once?
A standard-issue 2020 New Jersey license plate had one letter, then two digits, followed by three letters. New Jersey DOO SPA Garden State These plates were not allowed to have letters D, T, or X in the fourth position, or the letters I, O, or Q in any position. With these restrictions, how many different license plates were possible in 2020?
A bagel shop has bagels in the following six varieties: plain, sesame, onion, blueberry, asiagocheese, and everything. Assuming there are at least 20 bagels of each variety, how many waysare there to choose 20 bagels...a. with no restrictions.b. with three or fewer blueberry bagels.c. with three or fewer blueberry bagels and three or fewer onion bagels.
3. Mr. Jones intends to place 10 books on his bookshelves. Among these, 4 are books on mathematics, 3 are books on chemistry, 2 are books on history, and 1 is a book on a foreign language. Jones wants to arrange his books so that all the books dealing with the same subject are together on the shelf. How many different arrangements are possible?
a).A food-processing firm has 8 brands of seasoning agents from which it wishes to prepare a gift package containing 5 seasoning agents. How many combinations of seasoning agents are available? b). A sales person has 9 products to display in a trade fair but he can display only 4 at a time, how many displays can he make if the order in which he displays is important? c).A radio repairer notes that the time he spends on his job has an exponential distribution with a mean of 4 minutes. He follows the first come first serve principle. The arrival time of clients takes a Poisson distribution with an average rate of 8 clients every 1 hour. i.Determine the arrival rate value and service rate value to be used ii) How long will it take the client waiting in the queue iii). Determine the client’s average waiting time in the system iv).Compute the probability that the system is idle; P (idle)
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6. A jar is to be filled with 100 jelly beans. There are five varieties of beans to choose fromn and we are required to use between 10 and 50 beans of each variety. How many different ways of filling the jar are there?
2. If there are 120 people in your college class, are there at least 5 people that share the same last initial? a. Let the pigeon holes be: b. Let the pigeons be: c. What is k? d. Now the number of pigeons would have to be greater than: e. Is the number of pigeons or people greater? Why or why not? f. Are there at least 5 people that share the same last initial if there are 120 people in the college class? Why or why not? Write your response below:
a and b ??
The phone numbers on the Georgia Tech campus have the form SSS-CVA-TECH, where S can be the digits 1 to 9, C and H can be the digits 5 to 9, V and E can be any odd number from 1 to 9, A has to be the number 0, and T can be any digit. How many possible phone numbers?

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